Ordinals, Cardinals, Representation of Numbers in Language.

6-boxcomplete4Quoted from:  Pi in the Sky, by John Barrow. Oxford University Press, 1992. p. 37-38

  • “English: one/first ; two/second ; three/third ; four/fourth
  • French: un/premier ; deux/second or deuxième ; trois/troisième ; quatre/quatrième
  • German: ein/erste ; zwei/ander or zweite ; drei/dritter ; vier/vierte
  • Italian: uno/primo ; due/secondo ; tre/terzo ; quattro/quarto

In each of these four languages the words for ‘one’ and ‘first’ are quite distinct in form and emphasize the distinction between solitariness (one) and priority (being first). In Italian and the more old-fashioned German and French usage of ander and second, there is also a clear difference between the words used for ‘two’ and ‘second’, just as there is in English. This reflects the Latin root sense in English, French, and Italian of being second, this is, coming next in line, and this does not necessarily have an immediate association with two quantities. But when we get to three and beyond, there is a clear and simple relationship between the cardinal and ordinal words. Presumably this indicates that the dual aspect of number was appreciated by the time the concepts of ‘threeness’ and ‘fourness’ had emerged linguistically, following a period when only words describing ‘oneness’ and ‘twoness’ existed with greater quantities described by joining those words together as we described above.

In all the known languages of Indo-European origin, numbers larger than four are never treated as adjectives, changing their form according to the thing they are describing. But, numbers up to and including four are: we say they are ‘inflected’. […] a rather antiquated structure that barely survives in the modern forms of many Indo-European languages. For example, in French we find two words un and une corresponding to the English ‘one’ and they are used according to the gender of what is being counted. An analogous feature of language that certainly survives in English is the way in which different adjectives are associated with the same quantities of different things. We speak of a pair of shoes, a brace of pheasants, a yoke of oxen, or a couple of people, but we would never speak of a brace of chickens or a couple of shoes. […]

We have seen that the distinction between cardinal and ordinal aspects of number and the use of inflected adjectives is clear up to the number four but conflated beyond that. [Footnote: In Finnish there are still two kinds of plural, as in classical Greek, Biblical Hebrew and Arabic: one for two things and another for more than two. Also interesting in this respect is the fact that there is no connection between the words for ‘2’ and ‘½’ in the Romance and Slavic languages (nor in Hungarian which is not an Indo-European language) but in all the European languages the words for ‘3’ and ‘1/3’, ‘4’ and ‘1/4’ and so on, are closely related, just as they are in English. This may indicate that the concept of a fraction, or the relation between a number and the concept of a ratio, only emerged after counting beyond ‘two’.]


A curious speculation arises […] to give special status to the number 8 – the total number of fingers excluding the thumbs – that many known languages originally possessed a base-8 system (which they later replaced by something better), because the word for the number ‘nine’ appears closely related to the word for ‘new’ suggesting that nine was a new number added to a traditional system. There are about twenty examples of this link, including Sanskrit, Persian, and the more familiar Latin, where we can see novus = ‘new’ and novem = ‘nine’.”

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