The effect of cardinality in the pigeonhole principle

Bibliographic Data

ID21689129
AuthorsBenoît Jacquet (0000-0001-5310-2789, Université Paris 8, corresponding author), Jean Baratgin (0000-0001-9566-486X, Université Paris 8)
Year2024
Volume30
Issue1
Pages218-234
Publication date2024-01-02
Open AccessNo
TypeARTICLE
VenueThinking & Reasoning (JOURNAL)
Journal identifiersISSN: 1354-6783 • E-ISSN: 1464-0708
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/13546783.2023.2214377
OpenAlexW4378838174
LanguageEN
References cited30

The pigeonhole principle is a well-known mathematical principle and is quite simple to understand. It goes as follows: If n items are placed into m containers, and if m<n, then there must be at least one container with more than one item in it. A previous study by Mercier et al. yet found that participants tasked to solve a problem akin to this were unable to correctly solve it when the number n is understood as a quantity (cardinal) instead of an identifier (nominal). They suggest quantities first need to be turned into categories. We believe this difference can instead be explained by pragmatic factors not taken into account in their study. We disambiguate the problems given to participants and study the effects of their disambiguation and the influence of different kinds of quantities: countable and mass. We show that using a problem with countable quantities instead of hair, usually understood as non-countable, increase the performance of participants, no longer distinguishable from that of the nominal problem

Countable set · Data mining · Discrete mathematics · Epistemology · Generality · Identifier · Mathematical economics · Mathematical proof · Pigeonhole principle · Programming language · Cognitive and developmental aspects of mathematical skills · Computer Science · History and Theory of Mathematics · Mathematics · Mathematics Education and Teaching Techniques · Philosophy · Psychology

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