Naively, the world seems to be made up of objects that have definite, sharp boundaries. At least notionally, we assume we can draw a shape (perhaps a very wiggly one) around a region of space and say “everything within that shape is the table, everything outside it isn’t”.
It also seems perfectly plausible that we could take these sharply-defined objects and put them on top of each other, or otherwise “just in contact”. They don’t overlap (of course they don’t!) and nor do they float a sort of nonspecific distance apart (not if they’re properly touching). These are basic intuitions we have about objects in the world.
I think there’s a strong argument against these intuitions, and I think it suggests that objects, even very ordinary ones, can’t have sharp boundaries even in principle. It relies on some ideas about the space we live in, which you may or may not find intuitively appealing. It’s also an example of how I think philosophy can be done using mathematics. It’s pretty short. It’s here. It does require some maths, but nothing that couldn’t be explained with 15 minutes of hand-waving.
Pub Philosophy 