Ontology, the branch of metaphysics concerned with existence and being, asks a question that sounds almost too obvious to need asking at all: what does it actually mean for something to exist, and what kinds of things genuinely exist? A physical chair existing seems entirely uncontroversial. But the same question becomes genuinely difficult once it's applied to entities like numbers, abstract possibilities, or fictional characters — do these things exist in the same sense a chair does, in some different sense, or not really at all, and what would actually settle that question either way?
Physical objects don't exhaust every category ontologists have to account for
Ontology can't simply restrict its scope to physical objects, because a huge amount of ordinary discourse clearly refers to, and seems to make true or false claims about, things that aren't physical objects at all — mathematicians make claims about numbers that seem straightforwardly true or false, people discuss possibilities and hypothetical scenarios that never actually happened, and literary critics analyse fictional characters in ways that seem to say genuinely true things about them. Ontologists have to decide whether entities like these should be treated as genuinely existing, in some meaningful sense, or whether talk that appears to refer to them should instead be understood as not genuinely committing a speaker to those entities actually existing at all, despite how naturally and unavoidably such language shows up throughout ordinary discourse.
Different positions draw the boundary of existence in genuinely different places
Philosophers have staked out genuinely different positions on where to draw this boundary. Some argue that abstract entities like numbers exist in a real, mind-independent sense, just not as physical objects occupying space and time the way a chair does. Others argue that only concrete physical objects genuinely exist, and that apparent references to abstract entities should instead be understood as a kind of convenient shorthand that doesn't actually commit the speaker to those entities really existing. Still others propose intermediate positions, treating some non-physical categories, like genuine future possibilities, as existing in some meaningfully real sense while treating others, like specific fictional characters, quite differently. None of these positions has achieved anything close to full agreement across the field, which is a large part of why ontology remains such a genuinely active, unresolved area of philosophical inquiry rather than a settled, closed topic.
What we're still unsure about
That ontology grapples with genuinely difficult, unresolved questions about the existence of abstract and non-physical entities, and that philosophers have proposed several genuinely competing positions on where to draw the relevant boundaries, are well documented throughout the history and current state of metaphysics. What remains actively, fundamentally unresolved is which of these competing ontological positions, if any, is actually correct — this isn't a case of philosophers merely not yet having gotten around to settling an otherwise straightforward empirical question; the disagreement concerns what would even count as adequate evidence or argument for settling a question of this kind in the first place, which is precisely why ontological debates of this sort have persisted, in recognisably similar form, across centuries of sustained philosophical attention.
This sits inside Ontology: Being & Existence, one of seven topics in Metaphysics, one of five domains in Philosophy, one of seventeen subjects the app can quiz you on.