What Lloyd was describing there has a name in philosophy - "the paradox of the heap".

Most of the classification problems described here are a bit different - you don't just have one property varying along a continuum, but many conflicting features. Wittgenstein talks about that in the Philosophical Investigations, as "family resemblance" - a lot of concepts are ascribed in the same way you see people as being related, where two might share the same freckles, two might have the same wonky teeth, two might have the same eyebrows... you can tell everybody's related at a family gathering even though there's no one feature you can point to that makes them all look the same.