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Compositionality beyond bases.

Jean-Charles Pelland1

  • 1University of Bergen, 5015 Bergen, Norway.

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|October 20, 2025
PubMed
Summary

This study introduces "anchors" as a new framework for understanding number bases and compositional tools. This anchor-based approach offers a more inclusive and accurate way to discuss diverse numeration systems across different formats.

Keywords:
basecompositionalitynumeralsnumerical cognitionrecursionunit

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Area of Science:

  • Cognitive Science
  • Linguistics
  • Mathematics

Background:

  • Existing definitions of number bases in linguistics and notation studies are inconsistent, hindering a unified understanding of numeration systems.
  • Current definitions inadequately categorize diverse systems, either excluding too many or including too many under the 'base' umbrella.

Purpose of the Study:

  • To propose a novel conceptual framework using "anchors" (numbers as counting units) for a unified theory of compositional tools in numeration systems.
  • To demonstrate the limitations of existing definitions and the advantages of an anchor-based approach for format-independent analysis.

Main Methods:

  • Development of a new conceptual framework centered on "anchors" as counting units.
  • Analysis of perceptual grouping in tallies and place-value systems to illustrate shifts in counting units and recursive unit-labeling.
  • Application of the anchor-based framework to analyze lexical number systems.

Main Results:

  • The proposed anchor-based framework provides a more inclusive and accurate method for classifying numeration systems.
  • Demonstrates how perceptual grouping and place-value systems exemplify the core concepts of the anchor framework.
  • Highlights the framework's utility in analyzing well-established lexical systems.

Conclusions:

  • An anchor-based framework offers a superior, unified approach to studying compositional tools across all representational formats of numeration systems.
  • This framework resolves inconsistencies in existing definitions, enabling a broader and more accurate discussion of number bases.
  • The study contributes to a deeper understanding of the fundamental structures underlying human numerical cognition and representation.