I don't think "exist" means a single thing even in mathematics. For example, in second order logic I'd consider quantifying over elements in the domain of discourse to be different than quantifying over relations.
I would still consider this to be a single thing, the same way that "P and Q" is still a statement.
Phrasing this in different way when I say "exist" I mean "either exist in the sense of quantifying over relations or elements"(definition subject to revision as I learn more non-first order logic).
The 'Irrationality Game' posts in discussion came before my time here, but I had a very good time reading the bits written in the comments section. I also had a number of thoughts I would've liked to post and get feedback on, but I knew that being buried in such old threads not much would come of it. So I asked around and feedback from people has suggested that they would be open to a reboot!
I hereby again quote the original rules:
I would suggest placing *related* propositions in the same comment, but wildly different ones might deserve separate comments for keeping threads separate.
Make sure you put "Irrationality Game" as the first two words of a post containing a proposition to be voted upon in the game's format.
Here we go!
EDIT: It was pointed out in the meta-thread below that this could be done with polls rather than karma so as to discourage playing-to-win and getting around the hiding of downvoted comments. If anyone resurrects this game in the future, please do so under that system If you wish to test a poll format in this thread feel free to do so, but continue voting as normal for those that are not in poll format.