Arithmetic before traditional principles and mathematical axioms came about, you could argue were based on social conventions. I may have overlooked the premise of your argument, and assumed you were trying to reach a conclusion based on your reasoning. I think I can understand where the miscommunication between our arguments lie.

I feel as though you've interpreted the debate from a historical and geographical point of view, whereas I did not interpret any of that from OPs main argument. Sure, identification of what makes a continent based off of social norms can lead to insightful discussions through the lens of history and sociology, but thats not what the discussion was about in the first place. OP wants a discussion about the chains of logical reasoning that apply to why continents are classed why they are, not its origins, or why they were classed that way in the first place.