Beliefs about the nature of numbers

Lance J. Rips*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations


Nearly all psychologists think that cardinality is the basis of number knowledge. When they test infants’ sensitivity to number, they look for evidence that the infants grasp the cardinality of groups of physical objects. And when they test older children’s understanding of the meaning of number words, they look for evidence that the children can, for example, "Give [the experimenter] three pencils" or can "Point to the picture of four balloons." But when people think about the positive integers, do they single them out by means of the numbers’ cardinality, by means of the ordinal relations that hold among them, or in some other way? This chapter reviews recent research in cognitive psychology that compares people’s judgments about the integers’ cardinal and ordinal properties. It also presents new experimental evidence suggesting that, at least for adults, the integers’ cardinality is less central than their number-theoretic and arithmetic properties.

Original languageEnglish (US)
Title of host publicationMathematics, Substance and Surmise
Subtitle of host publicationViews on the Meaning and Ontology of Mathematics
PublisherSpringer International Publishing
Number of pages25
ISBN (Electronic)9783319214733
ISBN (Print)9783319214726
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Arts and Humanities(all)


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