If logical form systematically assigns hidden arguments (e.g., Davidson's event semantics assigns a fixed event variable to all action predicates), apparent arity variability is a syntactic illusion.

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Arity(as used in logic and linguistics): The number of things a word or concept needs to relate to in order to make sense. For example, 'is tall' needs one thing (you can be tall), but 'is taller than' needs two things (one person compared to another).
Davidson, Donald(as a key figure in philosophy of language and action theory): A 20th-century philosopher who developed influential theories about how language works, especially regarding actions and events.
action predicates(as used in philosophy of language): Words or phrases that describe what an action is or does, like 'runs,' 'speaks,' or 'teaches.'
arity variability(as used in linguistics and philosophy of language): The fact that some words seem to take different numbers of additional pieces of information (like how 'give' can mean 'give something' or 'give something to someone').

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event semantics(as used in philosophy of language)

A theory that treats actions as events (things that happen) and analyzes sentences about actions by including a reference to those events.

event variable(as used in formal semantics)

A placeholder in logical analysis that stands in for an event being described, similar to how 'x' might stand in for an unknown number in math.

hidden arguments(as used in semantics and linguistic analysis)

Parts of meaning that are implied or built into a sentence but aren't directly written or spoken.

logical form(Used to characterize logical consequence)

The way that a sentence is built up from the logical particles.

syntactic illusion(as used in philosophy of language)

Something that looks different on the surface level of language but is actually the same underneath when you analyze its structure.

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