>why do you agree that the conventional word "idea" can be used to signify both meanings, but then claim that the meaning is somehow very different.

Well I can only go by how the words are used. But when we're speaking rigorously, such ambiguities matter. The issue is that there are multiple ways these words are used. But when we try to use the casual meaning in more rigorous contexts, the discrepancies are important. When it comes to existence, people are purporting that there is an existence completely unlike physical existence, yet retains its centrality in our conception of the world and its constituents. I'm looking for clarity here. If we can't flesh out the nature of non-physical existence, we should refrain from using the term "exists" in those contexts.

ambiguity is an inescapable consequence of systems of communication based on social convention. That's really the fundamental reason why physicists have such a strong preference for mathematics. The convention there is of logic and notation rather than social preference and personal idiosyncrasy as with natural language.

but we don't have the means to use a rigorous system of communication when discussing consciousness. there is no calculus of mind. its not even clear that there could be, in principle.

so we need to re-calibrate our notion of rigor and precision to deal with the domain we're working in here. we shouldn't just wring our hands and lament that our communication tools fail us. we can still use them, we simply need to be more disciplined and avoid devolving into arguments about language semantics and conventions and try to focus on the actual content, ambiguous as it may seem.

here's a simple working definition of "existence" that may be ambiguous but should hopefully not be controversial. a thing exists if it is experienced by a conscious mind. this includes material things which are experienced via the conventional senses (sight, hearing, etc.). it also includes immaterial things, such as thoughts and ideas, which are experienced internally within a conscious mind.

this definition does not resolve the ambiguity regarding the point-of-origin of immaterial things, but that is not particularly relevant in my opinion. we don't need to answer that question in order to engage with the material, so let's just leave it unanswered.