Sometimes, even the earlist work (Aristotle) or the best (Linnaeus) may not be good enough later. We have concepts such as species, genus, family, etc. but the boundaries between them may not be so clear as previously thought. Back in the 1950s, I remember people drawing up relationships based on genotypic similarity rather than phenotypic. All the biologist that I knew thought this was a better way to do things. They were looking for relationships between entities rather than just classifications.
Here's an example of the impossibility of drawing (some) sharp boundaries between sets. A plausible criterion may be impossible to meet.
Take a set of entities each of which has 3 properties from a set of 7 (like diatonic chords?). There are 35 possible entities.
abc abd abe abf abg acd ace acf acg ade adf adg aef aeg afg
bcd bce bcf bcg bde bdf bdg bef beg bfg
cde cdf cdg cef ceg cfg
def deg dfg
efg
Now for example, assume that having two properties in common allow the entities to interbreed. Thus (abc abd abe abf abg) can interbreed, but abc and ade cannot. This is an example of a complex ring species.
The concept "can interbreed with" (equilalent here to "has two properties in common") doesn't seem quite right for "species" in this case. Also "can't interbreed with" doesn't make a really good boundary either.
Likewise a successive of single property changing progressions (keeping the two property breeding capacity) can move an entity abc through abe abf abd abg acg adg aeg afg bfg cfg dfg to efg which is rather far away "genetically."
More properties lead to similar results but with more complicated possibilities. All this happens with discrete items.