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Origins of Names of Ordinal and Cardinal Numbers

Date: 05/15/2002 at 22:51:26
From: Dr. Cliff Hesse
Subject: cardinal vs. ordinal numbers

This may be more of a semantics or linguistics question than one of 
math, but I thought that you might find it interesting:  Which may 
have originated first...ordinal or cardinal numbers?

I have discussed (in my class on "Communications, Technology and 
Culture") the fact that in almost every language, the word for the 
number "one" is almost always entirely different than the 
corresponding ordinal number - e.g., "first" in English. "Two" and 
"second" are not much closer, but "three" and "third" start to have 
some similarities and by "four/fourth" the two concepts reach a 
similarity of pronunciation and, often, spelling (but the individual 
concepts are still understood to be different). But which might or 
should have come first?

Date: 05/15/2002 at 23:37:46
From: Doctor Peterson
Subject: Re: cardinal vs. ordinal numbers

Hello, Dr. Hesse.

I don't know that I'm an expert on this, but it's interesting to look 
at the etymology of these words. Here is an answer I gave to a 
related question:

  >Do you know where the ST, ND, RD and TH come from when we 
  >write and say ordinal numbers...1ST, 2ND, 3RD etc?  I have 
  >a first grade student who wants to know.  Thank You.

  This isn't exacatly a math question, but I like languages too!

  Like many things in English (or other languages), such as 
  verb tenses, we have "regular" and "irregular" number words. 
  The simplest and oldest tend to follow their own odd patterns, 
  and when you get into the newer and bigger words a pattern 
  takes over. Clearly "-th" is the standard pattern for an 
  ordinal number; so where do the other endings come from?

  Actually, it's not just the endings but the whole words: 
  "fir-" and "seco-" don't exactly come from "one" and "two", 
  though you can see a connection between "third" and "three". 
  Let's look at each word individually, using the American 
  Heritage dictionary (which specializes in etymology) to 
  see where they come from.

  FIRST: This comes from Old English "fyrst". This is believed 
  to come from a Germanic word "furista", which in modern 
  English survives as "foremost". The "-st" is actually a 
  superlative ending ("-est").

  SECOND: This comes from Latin "secundus", meaning "following" 
  or "next". It's a participle of the verb "sequor", which means 
  "to follow" (as in  "sequel", "sequence", and "subsequent". 
  So the ending "-nd" is a Latin gerund ending.

  THIRD: This one finally comes from an English number: Old 
  English "thridda" comes from "thri", three. I don't know enough 
  Old English to know whether the "-d" is just a variant of the 
  "-th" in other ordinals ("-t" in Old  English), but it appears 
  that both are merely endings for ordinals.

  So we see that "first" and "second" are different because 
  they weren't originally ordinals at all, but special words 
  for two special positions in a sequence, the "front-most" and 
  the "next". "Third" almost falls into the normal pattern, and 
  then things become regular (and were in Old English as well:
  feortha, fifta, ...).

  Interesting, isn't it? Thanks for the question.

I would say that the words for cardinals and ordinals indicate not 
that one came before the other, but that they originated separately, 
with different purposes. And the difference (in English, at least) is 
not really a relic of the prehistoric development of Indo-European 
languages, but a relatively recent thing (after all, "second" is a 
borrowing from Latin). So I don't think we necessarily have any 
evidence of the sequence of events in ancient languages, but rather 
an evidence that small numbers were for a long time (and maybe still 
are?) perceived as something other than numbers in the full abstract 
sense. Consider also that in at least some languages "one" is hard to 
distinguish from the article "an", which does not carry a strong 
sense of number, just mere singularity.

- Doctor Peterson, The Math Forum 
Associated Topics:
Elementary Math History/Biography
Middle School History/Biography

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