Kind

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

For example, báq tuze means "soup" (or "soup-kind", or "soup in general") rather than sá tuze "some soup" or tú tuze "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 baı jí báq tuze, and only the result of our efforts (if we succeed) is sá tuze.

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 lä tuze 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 báq-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 sá or tú terms.
2. Individual-level predicates are true of their argument "no matter when": descriptions not tied to a timeline, like "___ is/are intelligent". A báq argument to such a predicate is interpreted as a general (but maybe not tú-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 báq argument to such a predicate is reduced to its sá 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 báq kato is to treat it the way you'd treat an indefinite noun phrase like "cats" in English.)

Formalization and theories

There remain some open questions on the exact working and formalization of báq and kind references. For example, does báq creates a logical scope, in such a way that changing its relative order of appearance with other quantifiers would yield different meanings? In e.g. “bu kaqgaı jí báq kato”, is the sometimes purported equivalency of báq with sá in stage-level slots denied, as it would mean there is a specific cat which I am not seeing? What should “he leqfuo báq kato áq” mean? Are kinds a separate ontological type?

One possible theory may be that the slot Carlson classes are a part of syntactic type of every predicates, and that báq expressions are expanded to different quantifier expressions depending on the Carlson class of the slot the expression goes in. This would open the possibility of báq expression having their own logical scope, for the better or the worse. This would also lend itself well to binding kind instances to anaphoric expressions, allowing “he leqfuo báq kato áq” to mean “cats lick themselves”.

Another possible theory may be that Carlson classes are mere lexicosemantic properties of predicates, so that syntax would not be aware of them, and that kind references would be intensional in nature, semantically homologuous to abstract properties referred to with cúaq expressions. Under such a model, predicates accepting báq complements would be provided with intensional arguments, and what is claimed about these intensions (e.g. making claims about intension themselves as with kind-level predicates, or making claims about instances as with stage-level predicates) would be fully up to the definition of the predicates themselves. This theory of intensionality would imply that báq expression would not create a scope interacting with that of other quantifiers, and would pretty much slip below the scope of any scope-creating elements, but it may implicate that expressing “cats lick themselves” is not as straightforwards as in alternative theories. It also opens issues of ontology, with respect to whether kind expressions belong to a separate type from that of concrete individual, and whether predicates accepting both kind and individual complements manifest type polymorphism or not, for example, whether “sá nuo” can either refer to a concrete individual or a kind, which could possibly cause unexpected issues with quantification. It might however be possible to have an ontological system by which the distinction between intensions (abstract properties) and extensions (concrete instances) is removed (by claiming that individuals are actually intensional properties with a single extension), which could possibly be helpful if mere type polymorphism is found to be source of semantic troubles.

The typical…

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