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 tủzȳ means "soup" (or "soup-kind", or "soup in general") rather than sa tủzȳ "some soup" or tu tủzȳ "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
[∀d: Dinosaur(d)] Extinct(d). Individual dinosaurs are not extinct, only dead. Dinosaurs, as a kind, are extinct. - "Cats are widespread" can not be expressed as
[∃c: Cat(c)] Widespread(c). Individual cats cannot be widespread on their own. - Even "I'll make some soup" can not be expressed as
[∃s: Soup(s)] WillMake(i, s). There isn't actually some instance of soup about which you're saying 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 tủzȳ, and only the result of our efforts (if we succeed) is sa tủzȳ.
One solution to this is to define predicates like "___ makes something satisfying property ___" and "The kind satisfying property ___ is extinct". But then we are really hiding our ability to talk about kinds in our vocabulary.
Semantics
When we fill an argument place with a kind term like baq tủzȳ, the logical meaning of the resulting claim depends on the Carlson class of the predicate with regards to that argument place:
- Kind-level places, such as in "___ are extinct" and "___ are widespread", which in a way make a direct claim about the kind, rather than any individuals of it.
- Individual-level...
- Stage-level...