15. Ké jıuchaqpatı / The birthday party
Numbers
The simplest Toaq numbers are made from the following words:
| Word | Meaning |
|---|---|
| koam | zero |
| shı | one |
| gu | two |
| saq | three |
| jo | four |
| fe | five |
| cı | six |
| dıaı | seven |
| roaı | eight |
| neı | nine |
| heı | ten |
In the falling tone, a number acts like a counting verb or adjective:
fe
▯ are five in numberNeı ké chaıbıo.
The teacups are nine.Cho jí ké lua gu.
I like the two stories.
In the rising tone by itself, it refers to an abstract quantity:
fé
the number fiveMa reutoaı sáq?
Is three a prime number?
In the rising tone and followed by a verb, it acts as an article:
fé kue
five booksZudeq jí jó zu.
I speak four languages.
Plural logic
Toaq is built on plural logic. We say a variable can refer to things, plural. For example, when we turn “The teacups are nine” into a formula, we might say: xx are teacups, and xx are nine. We don’t need to talk about a “set” of nine teacups.
What’s the point? Consider the following example. When we say “the students gathered”, it means they did so as a group. But “the students ate” means each individual student ate. In singular logic, we might put this as: gather(S), for some set of students S, and then ∀x ∈ S: ate(x). That is, we interpret “the students” differently in these two sentences. But then how do we make sense of “the students gathered and ate”? Maybe sets aren’t actually how language works.
If we embrace plurality from the ground up in our semantics, and say “xx are students, and xx gathered, and xx ate,” we can let the predicates themselves decide what to do with those plurals. Instead of talking about sets and membership, we take the relationship xx are among yy (written xx ≺ yy) as fundamental.
All this is why fe can just mean: “▯ are five in number.”
For more information, see Plural Quantification in the Standford Encyclopedia of Philosophy.
A plural tour of articles
Toaq’s sá corresponds to a plural existential quantifier ∃xx, so sá poq means “for some people xx.”
Kueq sá sıomche.
Some students gathered.
[∃xx: student(xx)] gather(xx)
But the universal quantifier we’ve been using, tú, is really the singular universal ∀x, meaning “for each x.” This just turns out to be what’s convenient a lot of the time. However, it does mean that you can’t meaningfully say:
Kueq tú sıomche.
Each student gathered.
[∀x: student(x)] gather(x)
There is another quantifier, tútu, corresponding to ∀xx. So tútu poq means “for any person or people xx,” but it doesn’t seem to come up often in everyday speech.
? Kueq tútu sıomche.
Any students gathered.
[∀xx: student(xx)] gather(xx)
This sentence still means something weird: if there are three students (A, B, and C), then it says “ABC gathered, and AB gathered, and AC gathered, and BC gathered, and A gathered, and B gathered, and C gathered.” Ranging over all pluralities is rarely what we want.
More useful is túq, an article which means something closer to all than to each. The phrase túq poq “all people” refers to the “maximal” xx that are people, in the sense that for any yy that are also people, yy ≺ xx.
Kueq túq sıomche.
All students gathered.
gather(xx), where student(xx) and [∀yy: student(yy)] yy ≺ xx
Some students gathered, and any students were among them.
All this to say: when we use a number as an article, it means the same thing as sá plus a counting verb, which is to claim the existence of some plural xx while restricting its number.
Kueq héı sıomche.
Kueq sá sıomche heı.
Ten students gathered.
∃xx: student(xx) and ten(xx) and gather(xx)
This means that Zudeq jí shí zu means “I speak a language” and not “I speak exactly one language.” We’ll learn how to say that some other time!
Counting higher
| Word | Meaning |
|---|---|
| heı | ten |
| guheı | twenty |
| guheı shı | twenty-one |
| fue | 100 |
| saqfue heı | 310 |
| saqfue guheı | 320 |
| saqfue cı | 306 |
The words for “twenty, thirty…” are made by compounding digits with heı. The words for “two hundred, three hundred…” are compounds ending in fue. To say two-digit and three-digit numbers, we put these parts next to each other to add them together. For example, 234 is gúfue saqheı jo (two-hundred thirty four). Only the first word gets the rising tone:
gúfue saqheı jo
Thousands, millions, decimals
To count even higher, we use the following “thousands separator” words:
| Word | Meaning |
|---|---|
| bıq | thousand |
| nhoeı | million |
| gıga | billion |
| tera | trillion |
If there’s no number before the thousands-word, shí is implied.
gúheı saq bıq jofue feheı cı
twenty-three thousand, four-hundred and fifty-six (23,456)nhóeı neıfue bıq
one million, nine-hundred thousand (1,900,000)
The word co is a spoken decimal point.
gú co saq koam jo
two point three zero four (2.304)
Dates
The names of the months are formed by adding jue to the numbers 1 through 12.
| Word | Meaning |
|---|---|
| shıjue | ▯ is a January |
| gujue | ▯ is a February |
| saqjue | ▯ is a March |
| jojue | ▯ is an April |
| fejue | ▯ is a May |
| cıjue | ▯ is a June |
| dıaıjue | ▯ is a July |
| roaıjue | ▯ is an August |
| neıjue | ▯ is a September |
| heıjue | ▯ is an October |
| heıshıjue | ▯ is a November |
| heıgujue | ▯ is a December |
By combining number words with chaq, we get words for the days of the month:
| Word | Meaning |
|---|---|
| fechaq | ▯ is a 5th of the month |
| saqheıshıchaq | ▯ is a 31th of the month |
You can talk about dates like so:
Rao ké patı ké fechaq po ké saqjue.
The party is on the 5th of March.
Poetic calendar
There’s also this alternative set of month names, where each month’s name is an alliteration based on nature or the month’s “role” in the year — the English back-translations below are just to give you an idea.
| Word | Meaning |
|---|---|
| chıochu | January – Newheart |
| luqluoq | February – Calmstead |
| ırue’ısıe | March – Galegrace |
| geagom | April – Hightorch |
| suaqsoq | May – Songpeak |
| nuoqnea | June – Mirrorwide |
| nharunhuo | July – Stormful |
| shuaqshoa | August – Giftdeep |
| reoruq | September – Huefall |
| feafao | October – Bravestop |
| hoehıu | November – Sunbrook |
| cuaocoa | December – Passbridge |