Nah, it's not pedantry, it's just a medievalist real tired of hearing people who don't actually deal with anything outside the modern world announcing how their phenomenon is oh so special and unique and the first time in history despite there being examples going back millennia.
I remind you that at no point do you explain why the Papacy isn't an international organization.
Problem is that International Organizations as such are defined in a myriad of law texts and peer-reviewed journals both in IR and Law studies which explicitly state that these are supposed to be made up of states, hence their name (
inter-national, between nations). The Papacy is not made up of nations; it does not have delegates from countries formally
representing said countries in its internal framework. Rather, it is much more akin to a forum if you will, where private citizens (who may or may not have backing from powerful factions) seek to steer the course of that forum's particular area of interest.
I understand your qualm with modernists, but as someone who has been teaching History of International Relations for 8 years I cannot help but take issue with having "international organizations" simply disregarded as some modernist mumbo jumbo. Note that even though since I finished my Master's in IR I have mostly dealt with said discipline when carrying out research, before that I did a Master's in History, so I can understand the feeling of political scientists and IR scholars monopolising some scholarly debates, even if I do not exercise the historian's trade nowadays.
Note, finally, that in my first post I said "International organizations do not
formally exist until the 19th Century"; I am fully aware that we can discuss the semantics of international organizations
informally existing before the 19th Century, but ultimately this falls within the parameters of contestative narratives. International organizations
formally emerge in the 19th Century.
Still, I meant the bit saying that your claim would warrant a dissertation. I, for one, would very much like to read at the very least a good paper on the subject!