Can we have non-propositional knowledge, for example knowledge of a predicate without a subject? I think an example would be: only this is now, which uses indexicals. I'm asking because I wonder whether we can have non-propositional knowledge of non-indexical present. Can we have non-propositional, but qualitative, knowledge of this sort?
I am guessing that "propositional" refers to the subject-predicate-object structure of traditional grammar. However, this structure is not semantically binding, we do use predicates with only nominal subjects (to satisfy the rules of grammar). This is what the "it is" construction and participles are for in English. For example, "it is raining" or "raining is occurring" have no semantic subject or object, there is no x that rains on y except for grammatical stand-ins like "it", at least not in the sentence. Descartes's cogito is often criticized for pulling the propositional subject, namely the "I", out of a hat when only "pure predicate" is warranted:
"The objection, as presented by Georg Lichtenberg, is that rather than supposing an entity that is thinking, Descartes should have said: "thinking is occurring." That is, whatever the force of the cogito, Descartes draws too much from it; the existence of a thinking thing, the reference to the "I", is more than the cogito can justify."
More generally, it is not particularly controversial that knowledge does not have to be propositionally framed, although the language of thought proponents, like Fodor, argue that in humans it is, in fact, so framed. But here is from Frank's Sentence Comprehension without Propositional Structure:
"Comprehending a sentence requires the construction of a mental representation of the situation the sentence describes... This paper presents a simple sentence comprehension model, consisting of a neural network that transforms sentences into representations of the events they describe. During training, the network develops internal representations of the sentences. An investigation of these representations reveals that they can encode propositional information without implementing propositional structure."
The idea of non-propositional knowledge is far more controversial, but there are many proponents that procedural knowledge (a.k.a. knowledge-how, see What is the relation between 'knowledge-that' and 'knowledge-how'?), and fewer that phenomenal knowledge (of qualia, etc., see Conee) are non-propositional. At least the former does not seem to be tied to the indexical present. In fact, the knowledge of qualia sounds like the closest thing to "non-propositional, but qualitative", and it can not be indexical if the Mary's room/knowledge argument is to work. So Mary's phenomenal knowledge of color red would be an example, if one accepts qualia.