How big is the smell of a baking pie? The concentration of pie molecules in the air is not a binary yes/no function of position, but at the same time the volume is definitely smaller than the county, and larger than the kitchen. Fuzzy-edged objects have some sense of size but there is some freedom in where to define their edge.
For the proton, the "size" is defined as a length-valued parameter in the function that expresses the charge distribution through space. The parameter is objective - but its association with the word "size" is imprecise. It is necessarily imprecise, not because of anything quantum or even unfamiliar, but because there's not another English word for the scale of objects without hard edges.
For the proton, the "size" is defined as a length-valued parameter in the function that expresses the charge distribution through space. The parameter is objective - but its association with the word "size" is imprecise. It is necessarily imprecise, not because of anything quantum or even unfamiliar, but because there's not another English word for the scale of objects without hard edges.