Kind

Toaq has a quantifier, baq, which is used to talk about kinds of things, rather than some or all instances of them.

For example, baq tủzy means "soup" (or "soup-kind", or "soup in general") rather than sa tủzy "some soup" or tu tủzy "all soup".

Why have kinds?

The need for a way to make claims about kinds is apparent from examples like the following:

• "Dinosaurs are extinct" can not be expressed as $\left[\forall D\colon {\text{Dinosaur}}(D)\right]{\text{Extinct}}(D)$. Individual dinosaurs are not extinct, only dead. Dinosaurs, as a kind, are extinct.
• "Cats are widespread" can not be expressed as $\left[\exists C\colon {\text{Cat}}(C)\right]{\text{Widespread}}(C)$. Individual cats cannot be widespread. Not even "many cats are widespread".
• Even "I'll make some soup" can not be expressed as $\left[\exists S\colon {\text{Soup}}(S)\right]{\text{WillMake}}({\text{I}},S)$. You aren't saying of some certain instance S of soup that you'll make it. Instead, the Toaq way of looking at this meaning of "make" is that we are "manifesting a kind". So we say bảı jí baq tủzy, and only the result of our efforts (if we succeed) is sa tủzy.

So, a language appears to need a way to make claims about kinds without quantifying over their individuals. One solution is to define predicates like "___ makes something satisfying property ___" and "The kind satisfying property ___ is extinct", and then fill them with tûzy ja. (This is the approach taken by pre-kind Toaq lıbaı, or Lojban jaukpa.) But then we are really just tucking away the grammatical concept of kinds in those English definitions. Moreover, it is unnaturally indirect for "X makes Y" to be a c 1 word when it very much feels like we are talking about things and not properties.

Semantics

When we fill an argument place with a baq-term, the logical meaning of the resulting claim depends on the Carlson class of the predicate with regards to that argument place.

1. Kind-level predicates, such as "___ are extinct" and "___ are widespread", just make a direct claim about the kind, rather than any individuals of it. They are usually nonsensical when filled with sa or tu terms.
2. Individual-level predicates are true of their argument "no matter when": descriptions not tied to a timeline, like "___ is/are intelligent". A baq argument to such a predicate is interpreted as a general (but maybe not tu-universal?) claim over the individuals of the kind: "cats are intelligent", i.e. (pretty much?) any cat is intelligent.
3. Stage-level predicates are true only of their argument in their current temporal stage. A baq argument to such a predicate is reduced to its sa equivalent: "cats are playing" means "some cats are playing".

(These classes originated in linguistics to describe the apparent variety in meanings an indefinite noun phrase like "cats" can take on in different sentences. So in a sense, an easy way to think about baq kảto is to treat it the way you'd treat an indefinite noun phrase like "cats" in English.)

Binding

Hoemai said in 2019 that baq pỏq does not introduce a scope, and does not bind a variable pỏq. Instead it behaves like a constant like jí or súq. It has also been proposed that baq pỏq could bind pỏq after all, so that a sentence like Chỏ baq shỉ pỏq shí pỏq could mean "People like themselves". The other possible sentence, "people like people", could still be rendered as Chỏ baq shỉ pỏq baq shỉ pỏq.

The typical…

baq does not mean "the typical X" (and never has). Typicality is orthogonal to baq: you can call individual three-leaf clovers "typical", or say that baq clover rarely has four leaves.

External links

• Hoemaı's "gist" about baq and Carlson classes on Discord
  Hoemaı:

    So, gist:
    There are three types of predicates when it comes to baq predication.
    1) Kind predicates
    2) stage level predicates
    3) individual level predicates
    These are properties of predicates, or more exactly, of their argument places.
    Depending on the place type, different things happen with baq.
    Kind predicates make claims about kinds themselves. These cannot be paraphrased using sa. Examples: dinosaurs are extinct != there exist some dinosaurs that are extinct; cats are widespread != there are some cats that are widespread; looking for gold != there is some gold such that I’m looking for it
    Using baq with stage level predicates can be reduced to sa. These are predicates that a otherwise used with non-baq arguments. (baq) cats are in my garden = there are some cats in my garden
    Individual level predicates are also predicates that basically use non-baq arguments. When using baq in those places, it can't be paraphrased using sa. dogs are smart != there are some dogs that are smart
    Summary: No matter which kind of predicate you're dealing with, every non-baq place can also be filled by a baq argument, but not every baq place can be filled by non-baq arguments.
    (There isn't that much left to spoil, other than the real reason why baq is a quantifier/determiner)