Cardinal numbers

Reconstruction of the Ancient Numeral System in Basque Language

Philology ◽

10.3726/phil042019.3 ◽

2019 ◽

Vol 4 (2018) ◽

pp. 157-172

Author(s):

FERNANDO GOMEZ-ACEDO ◽

ENEKO GOMEZ-ACEDO

Keyword(s):

Cardinal Number ◽

Counting System ◽

Cardinal Numbers ◽

Original Meaning ◽

Diachronic Development ◽

Insight Into

Abstract In this work a new insight into the reconstruction of the original forms of the first Basque cardinal numbers is presented and the identified original meaning of the names given to the numbers is shown. The method used is the internal reconstruction, using for the etymologies words that existed and still exist in Basque and other words reconstructed from the proto-Basque. As a result of this work it has been discovered that initially the numbers received their name according to a specific and logic procedure. According to this ancient method of designation, each cardinal number received its name based on the hand sign used to represent it, thus describing the position adopted by the fingers of the hand to represent each number. Finally, the different stages of numerical formation are shown, which demonstrate a long and diachronic development of the whole counting system.

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The Natural Numbers

10.1093/oso/9780199641314.003.0010 ◽

2018 ◽

Author(s):

Øystein Linnebo

Keyword(s):

Natural Number ◽

Peano Arithmetic ◽

Number Sequence ◽

Natural Numbers ◽

Ordinal Numbers ◽

Cardinal Numbers

How are the natural numbers individuated? That is, what is our most basic way of singling out a natural number for reference in language or in thought? According to Frege and many of his followers, the natural numbers are cardinal numbers, individuated by the cardinalities of the collections that they number. Another answer regards the natural numbers as ordinal numbers, individuated by their positions in the natural number sequence. Some reasons to favor the second answer are presented. This answer is therefore developed in more detail, involving a form of abstraction on numerals. Based on this answer, a justification for the axioms of Dedekind–Peano arithmetic is developed.

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