It isn’t that your definition is wrong, it’s just that the logical consequence of your definition is that what does not exist, does not in fact exist. Trying to say this is the equivalent of the proof discussed is either deliberately ingenuous, or proof that you lack any understanding of logic.
Tris
Truth seeker said: “One key point is that this particular proof doesn’t actually prove all the much.” and “In other words, we can use your definition. But all it proves is that, “That being which is just a figment of my imaginition does not exist in all possible worlds.” This is trivial since you are starting from the premise that this being does not exist in this world.”
Well, yes. That is pretty much the point I am trying to make.
If you start with any definition that you don’t have to demonstrate is a true definition, you can prove whatever you like, from Invisible Pink Unicorns to figments, Newton, to an omnicient and omnipotent god. And if you can prove anything you can’t really prove anything at all.
And Tris, I think that maybe I do have a very incomplete and primitive understanding of some logical processes, which is more than I can say for some of the theists on this board. There have been, what, two hundred fifty-odd messages on two threads, clouds of squiggles and brackets, avalanches of words, all coming down in the end to “a god exists because we define it as
existing.”
Your tone, by the way, really disappoints me. Somewhere above you demonstrated the moral courage to say, more or less, that you believe, even in the face of illogic, just because you believe. This while several other Xians were dancing around what I thought was a rather basic question, one that was presented by several other unbelievers as well as my self: How is it possible that, if there is only one god which presents itself in different aspects to different people, can some of its communications appear to be direct contradictions to others? You said that you don’t know, but you believe anyway. That is a viewpoint I can respect absolutely, even if I don’t agree with your conclusions.
I have always enjoyed your postings (and Polycarp’s), while wishing that there were more Xians who felt as you do. So, forgive me, but I am a little saddened when you get snappish.
Mapache,
I am sorry, the tone was unwarranted, and I apologize without reservation.
I still believe in logic, though. 
Tris
Truth
Indeed you can, and in fact you have. But now you have absolved your original strictly defined circle on a Euclidean plane of all analytic restrictions. Now, your object is no longer a circle, but is a synthesis of an ideal shape. If it resolves to a line segment in 1 dimension, and a circle in 2, then we can reasonably assume that in 3 dimensions, it will be a sphere, and in 4, a hypersphere. Or can we? Does the uber-point expand into a circle necessarily in 2 dimensions (thus sending it back to its analytic status of a thing with contingent rules)? Or is it possible that it might remain a line segment? Or even become a square?
If there is no contingency, then your Equaladron might expand into anything or nothing at all. But at least it will be synthetic, and you can prove ontologically that Shape exists in all possible worlds that have at least one point.
You may then, if you wish, step outside existential philosophy to speculate about what, if any, broader metaphysical implications your discovery might have.
Addressing the second issue first, I don’t see why a very commonplace application of an exluded middle ought to say anything at all about whether something is trivial, great, or otherwise.
As to the first issue, metaphors like “figment of the imagination” aren’t used in any logical system, and for good reason. They either don’t say anything meaningful or else they say too much; that is, they are amphibolous. If “figment of the imagination” means something that doesn’t exist or can’t exist, then it is a ridiculous term to use because it stands in direct contradiction to the definition, which speaks of existence. If, on the other hand, “figment of the imagination” means something that the mind can conceive (but not merely a nonexistent conception), then it is dead-on accurate. […shrug…] Who can say what it means?
Mapache
Oh, it’s fine so long as you let me know about it. I can do an internal translation whenever I see you use the term, along the lines of “Note to self: Mapache is not referencing the being I defined but rather something else.” I don’t have a problem with that, but you might have to remind me now and again.