The basis for it is a mathematical principal of a limit, wherein a mathematical object is defined as a value or geometric construct that arises from indefinitely approaching but never actually attaining a specific output value as the input changes, which is useful for working with transfinite or hypperreal numbers and results in math that is otherwise undefined, like calculus.
In a similar manner of thinking, I was looking at post-humanist arguments and found this recurring tendency to break down the boundaries between arbitrary distinctions with gradual vagueness; that there is no black and white, no distinction between two ideas such as human and machine, or living and non-living, male and female, etc.
This was initially as a response to colonial Eurocentricism by breaking down the boundaries between different races and to overcome gender discrimination. What it did was show the gradient of middle grounds between any two bodies of people in order to overcome discrimination by showing they are ultimately the same.
But, in an increasingly technological civilization, it has diffused into many other subjects.
For one example in Donna Haraway's Cyborg Manifesto and Catherine Hayle's many critiques of society, they both look at the idea of breaking down the barrier between human and machine by perpetually pushing the boundary between the two until they become indistinguishable. A person may modify themselves with inorganic components, like a handicapped person may use prosthetic limbs, but taken to a greater extreme a person may modify their sensory to perceive new senses like Niel Harbisson or modify their brain to take out or insert modes or thought and alter their own DNA with research from the CRISPR experiments. This leaves one with the concept of the "cyborg" as an entity that can qualify as both organic and machine, which, itself is along a similar line to the ever popular singularity. This asks a question such as "If a person can turn into a machine, where do you draw the line?" The lack of an answer to which leads one to the conclusion that both human and machine must be categorizable under one functional relationship.
Or take for instance with the distinction between animals and humans: one can argue that the boundary between the two has been broken as any aspect someone considers unique to humanity can be found in other animals: dolphins (and possibly elephants) are capable of language and complex thought, perrots or ravens and many other birds are capable of empathy, many carnivora and rodents like dogs and rats are capable planning and coordinating with each other, some primates as well as some birds and some cephalopods are capable of creating and/or using technology, etc. And, unsurprisingly, biologists scientifically classify all animals and humans under the same taxonomical kingdom "anamalia."
I have seen this kind of limit logic argument where, one construct can gradually but perpetually approach the definition of a similar construct or their distinction made gradually vague, the conclusion is that they are (in some way) inevitably the same. It occurs somewhat frequently, so I am wondering if there is a consensus on the proper term for this kind of vague boundary argument.