In Kant's famous division between a priori vs a postriori, and synthetic vs analytic, Kant's example for a priori analytic proposition is:
All bodies are extended.
Without immediately delving into the proposition itself, I'd like to ask why (if at all) Kant considers extendedness to be an a priori trait. I'll give a bit more context-
In later chapters Kant discuss one of the only a priori metaphysical objects (or subject?) - space (spatiality? Not sure about the proper English term). The proposition is quite simple: in order to think of anything we'd first need to contain it inside something, no matter if it's a thought or "physical" object (not sure if Kant would agree exactly to that sentencing, as it's more of a Spinozanian metaphysical space) - we always "imagine" it contained within some container, and even if we try to "get out" of that container -- we're simply ending up in a bigger container.
After taking space as an a priori metaphysical object, we need to discuss if extendedness (the ontology of physique, or "being in space") is also a priori metaphysical or a postriori (or maybe more precisely, analytic a priori or synthetic a priori). If we go to the direction that says extendedness is analytic a priori, I think it takes us more to a Leibnizian metaphysics rather than Kantian, so I'd have to assume Kant take extendedness to be synthetic a priori. But if extendedness is synthetic a priori, what does it mean to the quote above, as Kant gives it as analytic a priori? Or maybe the judgment itself on the link between body and extendedness is analytic a priori, but extendedness itself is really synthetic a priori?
I hope this isn't too convoluted.
