Original title: Srovnání logického a psychologického pojetí čísla.
Translated title: Comparison of logical and psychological perspectives on the concept of number.
Authors: Kuncová, Alexandra ; Punčochář, Vít (advisor) ; Kůrka, Petr (referee)
Document type: Bachelor's theses
Year: 2013
Language: eng
Abstract: [eng] [cze]
This paper is divided into three main parts. In the first part, we propose a logical approach to the concept of number based on Frege's Foundations of Arithmetic. Besides the main attempt to define and classify number per se, we also discuss Husserl's struggle with psychologism, Frege's logicism, and the construction of the series of natural numbers. In the second part, we look at a psychological approach to the concept of number through theories and experiments of cogni- tive science. We focus on infants' understanding of numbers and amounts, their counting abilities and later conventional skills. In the third part, we summarise differences as well as similarities of these two approaches. Keywords: cognitive science, concept, Frege, Husserl, identity, logicism, num- ber, one-to-one correspondence, Piaget, psychologism. "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." (Albert Einstein, Geometry and Experience, 1921) Táto práca je rozdelená na tri hlavné časti. V prvej časti predstavujeme logický prístup k pojmu čísla na základe Fregeho diela Základy Aritmetiky. Popri snahe definovať a klasifikovať číslo ako také, rozoberáme aj Husserlove ťažkosti s psy- chologizmom, Fregeho logicizmus, či konštrukciu postupnosti prirodzených čísel. V druhej časti sa pozeráme na psychologický prístup k pojmu čísla, a to cez teórie a experimenty kognitívnej vedy. Zameriavame sa na detské chápanie čísel a množstiev, ich schopnosť počítať a neskôr získané všeobecné znalosti. V posled- nej časti sumarizujeme rozdiely, ako aj podobnosti týchto dvoch prístupov. Kľúčové slová: číslo, Frege, Husserl, identita, kognitívna veda, pojem, logiciz- mus, Piaget, psychologizmus, vzájomne jednoznačná korešpondencia. "Kým zákony matematiky popisujú realitu, tak nie sú presné; a keď sú presné, tak nepopisujú realitu." (Albert Einstein, Geometry and Experience, 1921)
Keywords: cognitive science; concept; Frege; Husserl; identity; logicism; number; one-to-one correspondence; Piaget; psychologism; Frege; Husserl; identita; kognitívna veda; logicizmus; Piaget; pojem; psychologizmus; vzájomne jednoznačná korešpondencia; číslo

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/55406

Permalink: http://www.nusl.cz/ntk/nusl-324695


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses