Re: Types of numerals

Carsten Becker wrote:
>So what you have are two (or more) independent counting
>systems? E.g. one, two, three for the ordinals but aigh,
>wir, dorn for the ordinals (making up random
>English-sounding words)?
Well, sort of. I suppose the two systems could even do some interbleeding,
or maybe even be both derived from a common source - the main point would be
having the cardinals and ordinals on an equal tier when it comes to
derivational morphology.
A case-stacking system where every noun requires to be marked for
nom/acc/dat (or erg/abs/etc if you prefer) but can still be inflected for
other, less syntactic cases, would be analogous.


>  > One could then split the class of numerals into
>  > "cardinal-derived" vs. "ordinal-derived" - maybe even
>  > contrasting other series purely by their roots. This is
>  > almost trivial to extend into mathematical series (half
>  > vs. halfth), but it might be possible to carry it over to
>  > grammatical series too - eg. contrasting the
>  > (cardinal-derived) word "trio" with an (ordinal-derived)
>  > word meaning maybe something along the lines of "third
>  > member of a trio".
>
>What about "fourth member of a quartet", "fifth member of a
>quintet" etc. then? Would they have the same name?
Of course not, but they would be from the same series. The "--out of X
people" connotation might not be necessary, tho; unlike "three persons", the
expression "third person" doesn't rule out the existence of further people.


>  > ..And speaking of negative numbers, why doesn't -1 have a
>  > name on its own, but i does?
>
>I assume i = imaginary number? We haven't had that in Maths
>yet, though, but I heard of it. Why should -1 have a name of
>its own? Maybe like "one missing", "two missing", "three
>missing" etc. and "first missing", "second missing", ... ?
>Why then only -1? OK, you often use -1 and when forming
>negative values, you actually multiply numbers with -1 but
>don't write '-1·n' but only '-n' instead.
That's exactly what I mean. We have -1, -2, -3... but i, 2i, 3i... - not
"1i". The minus sign is not considered a unit as much as it is considered an
integral property of the number, yet i IS considered the "imaginary unit"
rather than just "imaginary 1".
It might have something to do with the fact that all other units always
remain when adding or subtracting - but for ALL "mathematical units", there
will exist purely numeric operations which can make them disappear into thin
air. The sign of a number merely is the most commonly encountered unit.

(I fully expect this not to make much sense to anyone without a good grasp
of the foundations of mathematics. The paradigm shift involved is quite
small anyway.)


>Uwjge is your conlang, isn't it?
Yes, as explained in a previous message.


>  > So what other numerals are there? English has at least the
>  > "group numerals" (single, duo, trio...), the "repeat
>  > numerals" (once, twice, thrice...)
>
>But English only has up to 'thrice' there AFAIK, I've never
>seen 'fource' and 'fifce' etc. yet. Would only add to the
>confusion between -teen and -ty since there's also -th and
>-ce then :-)
It is true that one has to resort to the expression "x times" for all other
x, but the three words still form a limited series (or, the beginning of an
infinite one.)


>That's my 2 ct for today,
>Carsten
"Ct"? Interesting, I've before only seen "c" and "cn" used.

John Vertical

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