Member Rara Avis
Glad you made a new post for this.
What we need to clarify right off, I think, is whether you're discerning between something physical or something conceptual. There's a huge difference between the two (although, as with anything, that too can be argued).
If there is a chair sitting in the middle of the room and you point to it, saying it does not exist isn't a paradoxical statement, it's a statement that is either a lie or a matter of perspective. If you recognize the chair does exist, saying it doesn't is a falsehood. If the chair is there but you do not recognize it as such, you can say it is non-existent.
Concepts, however, are a much different thing. You can't see them, you can't touch them, smell them... so how do you prove they exist in the first place? In science, the burden of proof isn't in saying something is non-existent, but rather that it exists in the first place. (Which of course ends up being the same thing if you can't prove that it DOES exist).
Look to your right and point out Time for me. Can you prove it exists? If you can't, it's non-existent.