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 http://mathforum.org/dr.math/
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